Just search the index.php template for 'Continue' and edit as necessary. It will look something like this:

Code: 
<?php the_content('Continue Reading >>'); ?>
It should really be within the Wordpress loop, usually like this:

Code: 
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
<?php the_content('Continue Reading >>'); ?>
<?php endwhile; else: ?> <p><?php _e('Sorry, no posts matched your criteria.'); ?></p> <?php endif; ?>